Maximally Connected and Super Arc-Connected Bi-Cayley Digraphs

Abstract

Let \(X = (V,E)\) be a digraph. \(X\) is maximally connected if \(\kappa(X) = \delta(X)\). \(X\) is maximally arc-connected if \(\lambda(X) = \delta(X)\). And \(X\) is super arc-connected if every minimum arc-cut of \(X\) is either the set of inarcs of some vertex or the set of outarcs of some vertex. In this paper, we prove that the strongly connected Bi-Cayley digraphs are maximally connected and maximally arc-connected, and most strongly connected Bi-Cayley digraphs are super arc-connected.